The author argues for a conception of mathematical proof which contradicts the too widespread idea according to which mathematicians would prove theorems mainly to establish their truth. In sharp contrast to the latter, the author argues that proofs have rather an epistemic function, and that, even when they are wrong or inadequate, they still remain the main source from which new concepts emerge and new theories are developed. Hence, the author suggests, it is in proofs, rather than in theorems, that mathematicians look for mathematical knowledge: proofs constitute its main repository, theorems being mainly tags for finding one’s way within it. Proofs, the author stresses, need to be distinguished from derivations. The latter are the topic of a mathematical domain: proof theory, which is devoted to their study. However, the nature and functions of mathematical proof as actually carried out by communities of mathematicians require another kind of analysis and remain a topic to be studied by philosophers of mathematics. The program for the study of proof outlined by the author opens perspectives that are quite important for renewing the historical description of the activity of proving.